Clever visual proof

There are as many yellow dots above the bottom row of the triangle as there are pairs of purple dots on the bottom row. To see this, note that every yellow dot determines a pair of purple dots by projecting it down to the left and to the right. Conversely, you can go up from any pair of purple dots up to a yellow dot.

9 thoughts on “Clever visual proof”

This looks very close to Triangular Numbers ( http://en.wikipedia.org/wiki/Triangular_number) and I also feel that it can be used to explain that if particular problem pattern falls into a Triangular number order, then it’s complexity grows n^2. n being the final row, you will end up increasing the number of yellow dots in the top triangle.